Unable to make all my files available offline onto new Mac

I've got a new iMac after the old one has just given up the ghost. All my files are fortunately backed up on Dropbox.  My back-up drive was unfortunately corrupted.  I've installed Dropbox on the new computer and all my files now appear but with "zero bytes".  
But there's a problem.  I can download each file onto the hard drive one at a time by opening and closing it, but this is impossibly time consuming to do for every single file!  
I have gone to Dropbox Preferences, then clicked Sync and then checked Available Offline - but still all my "zero bytes" files remain on line and don't download until I click on them.  
I'm sure there's a simple solution. Please can someone advise me how to find it?  Thanks.